Problem: $ A = \left[\begin{array}{r}1 \\ 0 \\ 2\end{array}\right]$ What are the dimensions of matrix $ A$ ?
The first dimension is the number of rows in the matrix. How many rows does $ A$ have? The second dimension is the number of columns in the matrix. How many columns does $ A$ have? So, $ A$ is a 3 $\times$ 1 matrix.